The function \(g(\mathbf {q})\)  can be interpreted as a probability to be at point
\(\mathbf {q}\)  in the collective space. The GCM+GOA provides a general framework to
compute the collective inertia tensor and various zero-point energy corrections
associated with the collective motion [1]}. Indeed, after using
the GCM ansatz (REF ) for the many-body wave function
\(\mathinner {|{\Psi }\rangle }\)  and inserting the GOA approximations
(REF )-(REF ), one can show (after some rather lengthy
derivations presented in [2]}, [3]}) that the expectation value
of the total energy \(\mathinner {\langle {\Psi |\hat{H}|\Psi }\rangle }\)  becomes
\(\mathinner {\langle {\Psi |\hat{H}|\Psi }\rangle }=\int d\mathbf {q} g^{*}(\mathbf {q}) \mathcal {H}_{\rm coll}(\mathbf {q})g(\mathbf {q}),\) 
